While I was trained in cultural materialism in my undergraduate years, decades ago, I have never read a text that was explicitly arguing for this approach over others despite my being introduced to a variety of other approaches.
Years later, I read this text. It's pretty thorough in that Harris basically runs through a kind of shopping list of any particular approach which might be able to explain culture.
The thing is, while the text is pretty detailed, Harris basically argues that his approach, cultural materialism, is more complete, flexible and realistic than other approaches... where other approaches (methods) fall short is that they fail to do what cultural materialism does. You can be sure too that Harris can't cover the whole gambit of what these other approaches can and can't do, but he offers no point of comparison other than cultural materialism as the "be all" solution. This is a little like someone who likes Ayn Rand argue that other philosophies fail because they aren't Randian, and in that sense it is highly problematic.
If I were to write this book (and I am not sure I would) -- but wanted to convey that cultural materialism was the best, I would give some background/history as to how this approach developed vs how other approaches developed along with assessing them with examples. While Harris offers some history, he doesn't seem completely aware of the how different approaches were developed with as different responses to various problems and that is also baggage that needs to be contended with.
Instead Harris, while starting off somewhat philosophical, eventually abandons this approach and only cites examples and shows where cultural materialism might be able to offer "more" to explain what other approaches cannot. This doesn't really address the philosophical gaps -- the structural problems/limits in how these different methodologies are, but Harris, in the last one hundred pages, doesn't seem too concerned about providing this deeper critique, he only wishes to cram in examples and convince people by sheer force. So that last part gets kind of boring. Harris could have used a more philosophical approach, but I am not sure he knows exactly how to do that, even though he's obviously well versed in anthropological methods.
I think this book would be a good introduction to cultural materialism, but it isn't really a definitive exploration of the subject matter. It would be good read for a smart college student, but a truly critical approach would need additional considerations and texts.